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RESEARCH PAPERS

Weight Functions of Radial Cracks in Hollow Disks

[+] Author and Article Information
George T. Sha, Chien-Tung Yang

Allison Gas Turbine Division, General Motors Corporation, P.O. Box 420, Indianapolis, Indiana 46206-0420

J. Eng. Gas Turbines Power 108(2), 403-413 (Apr 01, 1986) (11 pages) doi:10.1115/1.3239919 History: Received December 17, 1984; Online October 15, 2009

Abstract

Explicit nodal weight functions for both bore and rim radial cracks in a hollow disk are presented with special emphasis on the load independent characteristics of the weight functions that can eliminate the repeated finite element computations of the Mode I stress intensity factors (K I ) for a given crack geometry under different loading conditions. An analytical expression, which relates the explicit crack-face weight functions to the radial distance (rs ) from the crack tip along the crack face, is also provided for wide range ratios of crack length (a) to the difference between outer disk radius (Ro ) and inner disk radius (Ri ) [ 0.01 ≤ a/(Ro − Ri ) ≤ 0.8] . The accurate explicit weight functions of any crack length can be obtained easily with a cubic spline interpolation technique from an adequate set of explicit crack-face weight functions of discrete crack lengths. With the availability of the explicit crack-face weight functions for both the bore and rim cracks, the Mode I stress intensity factors under any complex loading conditions can be calculated accurately and inexpensively by a sum of worklike products between the equivalent “un-cracked” stress field and the interpolated crack-face weight functions. This equivalent uncracked stress field could include the body force loading of a rotating disk, thermal loading, complex residual stresses, the applied tractions at the crack face and other locations, and any combinations of these loading conditions.

Copyright © 1986 by ASME
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